In this paper, we obtain several sufficient conditions such that the higher-order commutators $I_{\alpha,b}^m$ generated by $I_\alpha$ and $b\in \textrm{BMO}(\mathbb{R}^n)$ is bounded from $L^p(v)$ to $L^q(u)$, where $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{n}$ and $0<\alpha<n$.